A novel 2+1+1 decomposition of space-time based on a nonorthogonal double foliation is worked out and applied for the Hamiltonian description of general relativity, recovering earlier results in the proper limit. The complexity of the formalism allows for an unambiguous gauge-fixing of spherically symmetric, static black hole perturbations in the effective field theory approach of scalar-tensor gravitational theories. This gauge choice is also the closest to the general relativistic Regge-Wheeler gauge
